Class 8 Maths NCERT - Chapter 3: Understanding Quadrilaterals
Detailed Summary Points
1. **Polygon**: A closed figure formed by three or more line segments. The line segments are called sides.
2. **Classification of Polygons**: Based on the number of sides: triangle (3), quadrilateral (4), pentagon (5), etc.
3. **Diagonals**: A line segment connecting two non-consecutive vertices of a polygon.
4. **Convex and Concave Polygons**: A convex polygon has all interior angles less than 180°. A concave polygon has at least one angle more than 180°.
5. **Regular and Irregular Polygons**: A regular polygon has all sides and angles equal. An irregular polygon does not.
6. **Angle Sum Property**: The sum of the interior angles of a polygon with 'n' sides is (n - 2) × 180°. For quadrilaterals, it's 360°.
7. **Types of Quadrilaterals**:
- Trapezium: One pair of opposite sides parallel.
- Parallelogram: Both pairs of opposite sides are parallel.
- Rhombus: All sides equal and opposite sides parallel.
- Rectangle: Opposite sides equal and all angles 90°.
- Square: All sides equal and all angles 90°.
- Kite: Two pairs of adjacent sides are equal.
8. **Properties of Parallelogram**:
- Opposite sides are equal and parallel.
- Opposite angles are equal.
- Diagonals bisect each other.
9. **Properties of Rhombus**:
- All sides equal.
- Opposite angles equal.
- Diagonals bisect each other at right angles.
10. **Properties of Rectangle**:
- Opposite sides equal and parallel.
- All angles are 90°.
- Diagonals are equal and bisect each other.
11. **Properties of Square**:
- All sides equal.
- All angles are 90°.
- Diagonals are equal and bisect each other at right angles.
12. **Properties of Kite**:
- Two pairs of adjacent sides are equal.
- One pair of opposite angles are equal.
- One diagonal bisects the other at right angles.
Sample Question Paper
1. Define a polygon. Give examples.
2. What is the angle sum property of a quadrilateral? Prove it.
3. Classify the following polygons: Triangle, Pentagon, Octagon.
4. Explain the difference between convex and concave polygons.
5. Name the types of quadrilaterals and write one property for each.
6. What are the properties of a parallelogram?
7. How is a rhombus different from a square?
8. Draw and label a kite. Mention its properties.
9. Prove that the sum of interior angles of a polygon with n sides is (n – 2) × 180°.
Hindi
सैंपल प्रश्न पत्र
1. बहुभुज को परिभाषित करें। उदाहरण दें।
2. एक चतुर्भुज का कोण योग गुणधर्म क्या है? इसे प्रमाणित करें।
3. निम्नलिखित बहुभुजों का वर्गीकरण करें: त्रिकोण, पंचभुज, अष्टभुज।
4. उत्तल और अवतल बहुभुजों के बीच अंतर समझाएं।
5. चतुर्भुजों के प्रकार नामांकित करें और प्रत्येक के लिए एक गुणधर्म लिखें।
6. समलंब चौकोण के गुणधर्म क्या हैं?
7. एक समद्विबाहु और एक वर्ग में क्या अंतर है?
8. एक पतंग का चित्र बनाएं और उसे चिह्नित करें। इसके गुणधर्म लिखें।
9. प्रमाणित करें कि एक बहुभुज के आंतरिक कोणों का योग (n – 2) × 180° होता है, जहाँ n बहुभुज की भुजाओं की संख्या है।
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